Squares are the numbers that are produced when a value is multiplied by itself.
If expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex] then the value exists [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex].
What is meant by square root?The radical symbol for the number's root is "√" in this instance. The square of the positive number is represented by multiplying it by itself.
Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root exists a value that, when multiplied by itself, returns the original value.
The original number can be attained by multiplying the square root of an integer by itself.
Only a perfect square number can have a perfect square root. Even perfect squares have an even square root. An odd perfect square will contain an odd square root. A perfect square cannot be negative and hence the square root of a negative number exists not defined.
Let the expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]
Now, [tex]$\sqrt{8}=\sqrt{2 \times 2 \times 2}=2 \sqrt{2}$[/tex]
[tex]$\sqrt{28}=\sqrt{2 \times 2 \times 7}=2 \sqrt{7}$[/tex]
therefore [tex]9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]
simplifying the given expression, we get
[tex]$=9 \sqrt{2}-3 \sqrt{7}+2 \sqrt{2}-2 \sqrt{7}$[/tex]
[tex]$=9 \sqrt{2}+2 \sqrt{2}-3 \sqrt{7}-2 \sqrt{7}$[/tex]
[tex]$=11 \sqrt{2}-5 \sqrt{7}$[/tex]
Therefore, the correct answer is option a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]
The complete question is:
Simplify [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]
a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]
b) [tex]$11 \sqrt{4}-5 \sqrt{14}$[/tex]
c) [tex]$6 \sqrt{5}$[/tex]
d) [tex]$6 \sqrt{9}$[/tex]
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jerry purchased a single family lot that measured 90' x 120'. the city requires a 20' setback on the front, a 15' setback along the sides and a 10' setback at the back of the lot. how big can jerry build his house?
The best measure of how big Jerry can build his house as required in the task content is; 60' by 90'.
Dimensions.It follows from the task content that the dimension of the family lot purchased by Jerry in a bid to build his house has dimensions; 90' × 120'.
Since the city requires 20' setback on the front and 10' setback at the back, it follows that the vertical length remaining and available to build his house is; 120' - 20' - 10' = 90'.
Also, the horizontal width available for him to build his house after the 15' setback along the sides is; 90' - 15' - 15' = 60'.
Therefore, the space available for Jerry to.build his house is; 60' × 90'.
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help me answer this question please
Answer:
sum = -15/2
Step-by-step explanation:
Given the formula for the n-th term of a sequence is n(n-8)/√(n+3), you want the sum of the 1st and 6th terms.
First termThe first term is found by substituting 1 for n:
1(1 -8)/√(1 +3) = 1(-7)/√4 = -7/2
Sixth termThe sixth term is found by substituting 6 for n:
6(6 -8)/√(6 +3) = 6(-2)/√9 = -12/3 = -4
SumThe sum of the first and sixth terms is ...
-7/2 +(-4) = -(7/2 +8/2) = -15/2
sum = -7 1/2
A man is lying on the beach, flying a kite. he holds the end of the kite string at ground level and estimates the angle of elevation of the kite to be 50
The kite's height above the earth is 287 feet.
A right-angled triangle is formed by the length of the string, the height of the kite (h) above ground, and the perpendicular distance from the end of the kite string to the man.
The link between the lengths and angles of a right-angled triangle is demonstrated through trigonometry.
Using trigonometric ratios,
the height of the kite above the ground is
sin(55) = h ÷ 350
h = 287 ft
As a result, the kite's height above ground is 287 feet.
A trigonometric function is a real function in mathematics that relates the angle of a right triangle to the ratio of the lengths of the sides. They are frequently used in earth sciences such as navigation, structural mechanics, astrophysics, geography, and many other fields.
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The function g(x)is represented by g (x)=2(x+3)^2+4.rewrite the function in standered form.
g( x ) = 2x² + 12x + 22 is the standard form of the the function g( x ) = 2( x + 3 )² + 4.
What is the standard form of the function?Polynomials in standard forms are written in a way that arrange the terms in descending order.
Given the data in the question.
g( x ) = 2( x + 3 )² + 4
First, we expand; ( x + 3 )² → ( x + 3 )( x + 3 )
g( x ) = 2( ( x + 3 )( x + 3 ) ) + 4
Using FOIL Method
g( x ) = 2( x² + 3x + 3x + 9 ) + 4
g( x ) = 2( x² + 6x + 9 ) + 4
Apply distributive property
g( x ) = 2( x² + 6x + 9 ) + 4
g( x ) = ( 2x² + 12x + 18 ) + 4
Add 18 and 4
g( x ) = 2x² + 12x + 18 + 4
g( x ) = 2x² + 12x + 22
Therefore, the function in standard form is g( x ) = 2x² + 12x + 22
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Rewrite in simplest terms: -4f-6(6f-10)
The given expression: -4f-6(6f-10) in simplified form
is: -40f + 60.
What is an algebraic expression and how is it simplified?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it. Simplifying the algebraic expressions is to carry out operations on the expressions and then clear it out.
Given, the expression for simplification is: y = -4f-6(6f-10)
Working on the expression above, we have:
y = -4f-6(6f-10) = -4f -36f + 60 = -40f + 60
Therefore the given expression: -4f-6(6f-10) in simplified form
is: -40f + 60.
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You have to write an equation then solve.
what is the answer to 2y=3x+4
Answer:
y = (3/2)x + 2
assuming that the question is to find y in its simplest form.
Step-by-step explanation:
2y=3x+4
(1/2)*(2y)= (1/2)*(3x+4)
y = (3/2)x + 2
The triangle shown is dilated with scale factor =2 which is the image of vertex m after the dilation
ANSWER
(-4, 2)
(Option D)
EXPLANATION
The triangle in the picture is dilated with scale factor 2.
This simply means that the size of the triangle was increased by 2.
To do this, first, let us write out the cordinates of the vertices of the original triangle:
M(-2, 1)
P(2, -2)
A(3, 5)
To dilate this, we will multiply the cordinates by 2, they become:
M' (-4, 2)
P' (4, -4)
A' (6, 10)
Therefore, the vertex M on the image after the dilation is (-4, 2).
(Option D)
Malika buys 20 bottles of cranberry juice at the corner store for a total cost of $20. If each bottle costs the same amount, how much is each bottle of juice?
Answer: 1 dollar per bottle
Step-by-step explanation:
If they cost $20 and she bought 20 bottles, we can use division.
$20 / 20 bottles = 1 dollar per bottle
Use spinner and color key to find the indicated probabilities. Landing on green or a vowelNot landing on yellow or a constant
Solution:
The spinner has a total of 8 sections.
There are two green sections and 4 four vowel sections where one of the vowels is also green.
Then, the probability of landing on green or a vowel is;
[tex]\frac{5}{8}=0.625[/tex]Help on this question
Answer: Yes
Step-by-step explanation: 250-250
An outlier is when some of the data is spread farther away from the rest of the data. It is far off from other data
Question 2 of 10
Multiply the following complex numbers:
(4-6) (6-8)
OA. -24-68i
OB. 72 +68i
O C. -24 +68/
OD. 72-68i
-24-68i is solution of complex number.
What is the best definition of a complex number?
Complex numbers are those that are expressed as a+ib, where a, b are actual numbers, and I is a fictitious number termed a "iota."Real and imaginary components are split into two separate numbers, which are referred to as complex numbers. The foundation of more complex mathematics, like algebra, are complex numbers. They have numerous practical applications, particularly in the fields of electronics and electromagnetism.(4-6i)(6-8i)
= 24-32i-36i+48i²
= 24 + -68i - 48
= -24-68i
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The complete question is -
Multiply the following complex numbers (4-6i)(6-8i)
someone please help me!!!
Im going to answer for the first one.So angles 1 and 2 are corresponding angles and so they are equal because line k and line p and parellel
Find an equation of the line parallel to the graph of y = -5x-3 that passes throughthe point of (3,2). Write your equation in slope-intercept form.
Parallel lines has the same slope. In our case, the slope is -5. Then, the searched line has the form:
[tex]y=-5x+b[/tex]where b is the y-intercept.
We can find b by substituting the given point (3,2) into the las equation. Then, we have
[tex]2=-5(3)+b[/tex]which gives
[tex]\begin{gathered} 2=-15+b \\ 2+15=b \\ 17=b \end{gathered}[/tex]Therefore, the parallel lines is given by
[tex]y=-5x+17[/tex]A grain tank on a farm is composed of a storage portion in the shape of a cylinder anda cone-shaped dispensing area at the bottom. The bottom cone portion has a slantheight of 5.5 feet. The entire exposed surface of the tank is to be painted. What is theapproximate amount of surface area that will receive the painting?8.4 ft12 ft5.5 ft
To fidn the surface area of the grain tank you need to find the area of:
Cylinder (without one of the bases as there are just one base exposed), use the next formula:
[tex]A_1=\pi\cdot r^2+h(2\pi r)[/tex]You have for the given cylinder:
h=12ft
r: as the diameter is 8.4ft the radius is 8.4tf/2=4.2ft
[tex]\begin{gathered} A_1=\pi(4.2ft)^2+12ft(2\pi(\text{4}.2ft)) \\ =17.64\pi ft^2+100.8\pi ft^2 \\ =118.44\pi ft^2 \end{gathered}[/tex]Cone (without the base as the base is not exposed), use the next formula:
[tex]A_2=\pi\cdot r\cdot s[/tex]You have for the given cone:
r= 4.2ft
s= 5.5ft
[tex]\begin{gathered} A_2=\pi(4.2ft)(5.5ft) \\ =23.1\pi ft^2 \end{gathered}[/tex]The entire exposed surface of the tank is:
[tex]\begin{gathered} A_T=118.44\pi ft^2+23.1\pi ft^2 \\ \\ =141.54\pi ft^2 \\ \\ \approx444.66ft^2 \end{gathered}[/tex]The approximate amount of surface area that will receive the painting is 444.66 squared feetsWhat is the value of the expression below when z=3?
10z^2 +7z+4
The value of the expression [tex]10z^2[/tex]+7z+4 when z = 3 is 115
The expression is
[tex]10z^2[/tex]+7z+4
The expression is defined as the statements that have a minimum of two terms containing numbers or variables , connected by an operator in between. The operator maybe addition, subtraction, division, multiplication etc..
The expression is
[tex]10z^2[/tex]+7z+4
The value of z = 3
Substitute the value of z in the given expression
= [tex]10(3)^2[/tex]+ 7×3 + 4
= 10×9 + 21 + 4
Multiply the terms first
= 90 + 21 + 4
Add them together
= 115
Hence, the value of the expression [tex]10z^2[/tex]+7z+4 when z = 3 is 115
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You will have $ in ten years if you set aside $500 a year at 10%.
Compound interest: $8,765.58
A rental car company charges $37.50 per day to rent a car and $0.05 for every mile
driven. Alyssa wants to rent a car, knowing that:
. She plans to drive 100 miles.
. She has at most $200 to spend.
Write and solve on
Hello!
Knowing that Alyssa wants to rent a car where the company charges $37.50 per day to rent a car and $0.05 for each mile driven we have to find out how many days she is planning on renting a car for.
Step-by-step explanation:
Using the information we have we can see that it will be an additional $5 based on how many miles she is planning on driving.
If the base cost to rent a car is $37.50 you will have to add an additional $5 for the number of miles she plans to drive making the total $42.50.
Since she has at most $200 to spend on a car rental she can rent a car for a total of 5 days at a total cost of $192.50
[tex]37.50[/tex] × [tex]4=150[/tex] + [tex]42.50[/tex] = [tex]192.50[/tex]
Hope this helps!
The inequality will be 37.5x + (0.05 ×100) ≤ 200, and Alyssa can afford 5.2 days to rent while staying within her budget
How to write and solve an inequality to determine the number of days?Given that the rental car company charges $37.50 per day to rent a car and $0.05 for every mile driven
She plans to drive 100 miles and has at most $200 to spend.
Let x is the number of days, Alyssa can afford to rent while staying within her budget
The inequality can be written as;
37.5x + (0.05 ×100) ≤ 200
Now solve for x:
37.5x + (0.05 ×100) ≤ 200
37.5x + 5 ≤ 200
37.5x ≤ 200 - 5
37.5x ≤ 195
x ≤ 195/37.5
x ≤ 5.2
Therefore, she can afford 5.2 days to rent while staying within her budget.
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Find the mean for the data set. 6, 14, 7, 4, 12, 8, 13, 4, 18, 14
Answer:
Concept:
Mean is just another name for average. To find the mean of a data set, add all the values together and divide by the number of values in the set. The result is your mean!
The values are given below as
[tex]6,14,7,4,12,8,13,4,18,14[/tex]The image below shows how to calculate the mean
By substituting values, we will have
[tex]\begin{gathered} \bar{x}=\frac{\sum ^{}_{n\mathop=0}x}{n} \\ n=10 \end{gathered}[/tex][tex]\begin{gathered} \bar{x}=\frac{6+14+7+4+12+8+13+4+18+14}{10} \\ \bar{x}=\frac{100}{10} \\ \bar{x}=10 \end{gathered}[/tex]Hence,
The mean = 10
To calculate the variance, we will use the formula below
[tex]^{}\sigma^2=\frac{\sum ^{\infty}_{n\mathop=0}(x-\bar{x})^2}{n}[/tex][tex]\begin{gathered} \sigma^2=\frac{\sum ^{\infty}_{n\mathop{=}0}(x-\bar{x})^2}{n} \\ (x-\bar{x})^2=(6-10)^2+(14-10)^2+(7-10)^2+(4-10)^2+(12-10)^2+(8-10)^2+(13-10)^2+(4-10)^2+(18-10)^2+(14-10)^2 \\ (x-\bar{x})^2=16+16+9+36+4+4+9+36+64+16 \\ (x-\bar{x})^2=210 \end{gathered}[/tex][tex]\begin{gathered} \sigma^2=\frac{\sum ^{\infty}_{n\mathop{=}0}(x-\bar{x})^2}{n} \\ \sigma^2=\frac{210}{10} \\ \sigma^2=\frac{210}{10} \\ \sigma^2=21 \end{gathered}[/tex]Hence
The variance = 21
To calculate the standard deviation,
[tex]\begin{gathered} \sigma=\sqrt[]{variance} \\ \sigma=\sqrt[]{21} \\ \sigma=4.58 \end{gathered}[/tex]Hence,
The standard deviation is = 4.58
A rectangular toolbox has a length of 20 inches, The width of the toolbox is 7 inches and it's height is 7.5 inches. How much metal would be needed to make the toolbox?
ok
I'll calculate the surface area to answer your question.
Area of the base and top = 2x20x7 = 280 in^2
Area of the frontal and behind faces = 2 x 7x7.5 = 105 in^2
Area of the left and right faces = 2x20x7.5 = 300 in^2
Total area = 280 + 105 + 300
= 685 in^2
The amount of wood needed is 685 in^2
Plot the ordered pair and state which quadrant or on which axis the point lies
Answer:
Explanation:
Given the ordered pair (-2, 4 1/2), where x = -2 and y = 4 1/2 = 9/2 = 4.5. Plotting this point, we'll have;
Note that quadrants are numbered in an anti-clockwise manner with the top right portion of the graph as Quadrant I. Looking at the plotted point, we can see that it lies in Quadrant II.
The total cost (c) in dollars of renting a car and driving it m
miles is given by the equation: c=15+2m. If the total cost
was $225, how far was the car driven?
The car was driven 105 miles.
What is rent?
An agreement where a fee is paid for the temporary use of a good, service, or property owned by another is known as renting, sometimes known as hiring, or letting.
In the given example the cost function is, c = 15 + 2m
Where, c is the total cost and m is the number of miles car driven.
The total cost was $225.
So, plug c = $225 in the above equation.
225 = 15 + 2m
210 = 2m
m = 105
Therefore, the car was driven 105 miles.
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Use the graph of f below. Assume the entire function is graphed below.Find ƒ(−1).ƒ(−1) = 0ƒ(−1) = −3ƒ(−1) = −1ƒ(−1) = −5
Answer:
ƒ(−1) = −3
Explanation:
From the graph, we have the point (-1, -3).
This means that:
• When x=-1
,• The value of f(x)=-3.
Therefore, the value of f(-1) is -3.
the area of a rectangular garden in square is xsquare -5x-300 If x=45 what is the width and the height of the garden 12a.widthheight 12b.please pot it step by step show all your work thank you
If a rectangle has an area of A and sides b and h, then:
[tex]A=b\cdot h[/tex]Solving for the base:
[tex]b=\frac{A}{h}[/tex]Basically, the sides b and h could have any value provided that b*h=A.
Nevertheless, this problem seems to want from us to factorize the expression:
[tex]x^2-5x-300[/tex]So that each side is a binomial.
Part a)
To factorize that expression, find two numbers so that if they are added up, the sum is equal to -5, and if they are multiplied, the product is equal to -300.
Since the product is negative, one number must be negative. Since the sum is negative, the biggest number should be the negative one.
Consider the factors of 300:
[tex]300=2\cdot2\cdot3\cdot5\cdot5[/tex]Using those factors, we can find pairs of numbers that give 300 as a result from multiplying.
After a bit of trial and error, notice that 15*20=300. If we choose 20 as the negative number, then 15*(-20)=-300 and 15+(-20)=-5. Therefore:
[tex]x^2-5x-300=(x+15)(x-20)[/tex]So, we can choose the width and the height to be those factors. Since (x+15) is greater then (x-20), then:
[tex]\begin{gathered} \text{Width}=x+15 \\ \text{Height}=x-20 \end{gathered}[/tex]Part b)
If x=45, then:
[tex]\begin{gathered} \text{Width}=60feet \\ \text{Height}=25feet \end{gathered}[/tex]I need your help please
In order to calculate the price for each brand, calculate the quotient in between the price for n forks over the number of forks, just as follow:
Brand A:
3.89/72 = 0.05
Brand B:
6.62/96 = 0.07
Hence:
Unit price for brand A:
$0.05
Unit price for brand B:
$0.07
Determine the distance between the points (−4, −7) and (−8, −13).
Answer:
2[tex]\sqrt{23}[/tex]
Step-by-step explanation:
The distance between the points (-4, -7) and (-8, -13) is 2√13 units as per the concept of distance between the two points.
To determine the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is as follows:
[tex]Distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)[/tex]
Given the two points (-4, -7) and (-8, -13), we can assign the coordinates as follows:
x1 = -4, y1 = -7 (coordinates of the first point)
x2 = -8, y2 = -13 (coordinates of the second point)
Now, we substitute these values into the distance formula:
[tex]Distance = \sqrt{(-8 - (-4))^2 + (-13 - (-7))^2)}\\\\= \sqrt{((-8 + 4)^2 + (-13 + 7)^2}\\= \sqrt{((-4)^2 + (-6)^2)}[/tex]
= √(16 + 36)
= √52
= 2√13
Therefore, the distance between the points (-4, -7) and (-8, -13) is 2√13 units.
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For A Brainlist !! Please Help Iwill Mark Brainlist I appreciate it so much I think its D but im not sure
The operations which must be part of the inverse function g(x) are:
Add 3Divide by 2.What is an inverse function?An inverse function can be defined as a type of function that is obtained by reversing or undoing a mathematical operation in a given function (f(x)).
In Mathematics, a given function (f(x)) and its inverse function has the following property f⁻¹(f(x)) = x.
Generally speaking, the inverse of multiplication is division while addition is the inverse of subtraction. In this context, we can reasonably and logically deduce that a "division by 2," followed by an "addition of 3" to the function f(x) are the operations that must be part of the inverse function g(x).
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which two county libraries charge the same penalty per week
Answer:
where's the rest of the question⁉️
according to a survey of advanced curriculum high school students, the mean time spent studying each day is 6.4 hours. assume the standard deviation is 0.80 hours and that the probability distribution is normal. what is the 80th percentile for number of hours spent studying each day? round your answer to 2 digits after the decimal.
The 80th percentile for the number of hours spent studying each day is 7.07 hours.
A data set with a normal distribution has the majority of its values clustered in the middle of the range, while the remainder taper off symmetrically toward either extreme. The term "standard deviation" refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are dispersed when the standard deviation is high.
The percentage of scores below a given value is shown by percentiles. They provide information about how a score compares to other scores.
Given Data :
Mean time (u) = 6.4 hour
Standard Deviation = 0.80 hour
It is given that the probability distribution is normal.
The formula for the z-score is z =( x- mean)/standard deviation
For the 80th percentile, the z value from the z table is 0.842.
We have,
0.842 = (x - 6.4)/0.8
0.842*0.8 = x - 6.4
0.6736 =x - 6.4
x = 0.6736 + 6.4
x = 7.0736
x = 7.07
Hence, the 80th percentile for the number of hours spent studying each day is 7.07 hours.
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Tara makes two batches of purple food coloring. The table show the number of drops of red and blue coloring she uses for each batch. Do the two batches use the same number of drops of red per drop of blue.
Given data:
The number of red drops for first batch are r=100.
The number of blue drops for first batch are b=20.
The number of red drops for second batch are r'=75.
The number of blue drops for second batch are b'=15.
The expression for the red per blue drop for first batch is,
n=r/b
Substitute the given values in the above expression.
n=100/20
=5
The expression for the red drop per blue drop of the second batch is,
n'=r'/b'
Substitute the given values in the above expression.
n'=75/15
=5
Thus, yes the ratio of red to the blue drop is same for both batches.
